Updating parallel options pricing example.

docs/examples/parallel/options/Parallel MC Options.ipynb

@@ -0,0 +1,512 b''
+{
+ "metadata": {
+  "name": "Parallel MC Options"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Parallel Monto-Carlo options pricing"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "This notebook shows how to use `IPython.parallel` to do Monte-Carlo options pricing in parallel. We will compute the price of a large number of options for different strike prices and volatilities."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Problem setup"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "%pylab inline"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "\n",
+        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
+        "For more information, type 'help(pylab)'.\n"
+       ]
+      }
+     ],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "code",
+     "collapsed": true,
+     "input": [
+      "import sys\n",
+      "import time\n",
+      "from IPython.parallel import Client\n",
+      "import numpy as np"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Here are the basic parameters for our computation."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": true,
+     "input": [
+      "price = 100.0  # Initial price\n",
+      "rate = 0.05  # Interest rate\n",
+      "days = 260  # Days to expiration\n",
+      "paths = 10000  # Number of MC paths\n",
+      "n_strikes = 6  # Number of strike values\n",
+      "min_strike = 90.0  # Min strike price\n",
+      "max_strike = 110.0  # Max strike price\n",
+      "n_sigmas = 5  # Number of volatility values\n",
+      "min_sigma = 0.1  # Min volatility\n",
+      "max_sigma = 0.4  # Max volatility"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "code",
+     "collapsed": true,
+     "input": [
+      "strike_vals = np.linspace(min_strike, max_strike, n_strikes)\n",
+      "sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "print \"Strike prices: \", strike_vals\n",
+      "print \"Volatilities: \", sigma_vals"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Strike prices:  [  90.   94.   98.  102.  106.  110.]\n",
+        "Volatilities:  [ 0.1    0.175  0.25   0.325  0.4  ]\n"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Monte-Carlo option pricing function"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The following function computes the price of a single option.  It returns the call and put prices for both European and Asian style options."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def price_option(S=100.0, K=100.0, sigma=0.25, r=0.05, days=260, paths=10000):\n",
+      "    \"\"\"\n",
+      "    Price European and Asian options using a Monte Carlo method.\n",
+      "\n",
+      "    Parameters\n",
+      "    ----------\n",
+      "    S : float\n",
+      "        The initial price of the stock.\n",
+      "    K : float\n",
+      "        The strike price of the option.\n",
+      "    sigma : float\n",
+      "        The volatility of the stock.\n",
+      "    r : float\n",
+      "        The risk free interest rate.\n",
+      "    days : int\n",
+      "        The number of days until the option expires.\n",
+      "    paths : int\n",
+      "        The number of Monte Carlo paths used to price the option.\n",
+      "\n",
+      "    Returns\n",
+      "    -------\n",
+      "    A tuple of (E. call, E. put, A. call, A. put) option prices.\n",
+      "    \"\"\"\n",
+      "    import numpy as np\n",
+      "    from math import exp,sqrt\n",
+      "    \n",
+      "    h = 1.0/days\n",
+      "    const1 = exp((r-0.5*sigma**2)*h)\n",
+      "    const2 = sigma*sqrt(h)\n",
+      "    stock_price = S*np.ones(paths, dtype='float64')\n",
+      "    stock_price_sum = np.zeros(paths, dtype='float64')\n",
+      "    for j in range(days):\n",
+      "        growth_factor = const1*np.exp(const2*np.random.standard_normal(paths))\n",
+      "        stock_price = stock_price*growth_factor\n",
+      "        stock_price_sum = stock_price_sum + stock_price\n",
+      "    stock_price_avg = stock_price_sum/days\n",
+      "    zeros = np.zeros(paths, dtype='float64')\n",
+      "    r_factor = exp(-r*h*days)\n",
+      "    euro_put = r_factor*np.mean(np.maximum(zeros, K-stock_price))\n",
+      "    asian_put = r_factor*np.mean(np.maximum(zeros, K-stock_price_avg))\n",
+      "    euro_call = r_factor*np.mean(np.maximum(zeros, stock_price-K))\n",
+      "    asian_call = r_factor*np.mean(np.maximum(zeros, stock_price_avg-K))\n",
+      "    return (euro_call, euro_put, asian_call, asian_put)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We can time a single call of this function using the `%timeit` magic:"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "%timeit -n1 -r1 print price_option(S=100.0, K=100.0, sigma=0.25, r=0.05, days=260, paths=10000)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "(12.217720657772686, 7.4170971244322672, 6.8120985432589185, 4.3727039632512152)\n",
+        "1 loops, best of 1: 236 ms per loop\n"
+       ]
+      }
+     ],
+     "prompt_number": 24
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "## Parallel computation across strike prices and volatilities"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The Client is used to setup the calculation and works with all engines."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": true,
+     "input": [
+      "c = Client(profile=\"default\")"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 12
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "A `LoadBalancedView` is an interface to the engines that provides dynamic load\n",
+      "balancing at the expense of not knowing which engine will execute the code."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": true,
+     "input": [
+      "view = c.load_balanced_view()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 13
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Submit tasks for each (strike, sigma) pair. Again, we use the `%%timeit` magic to time the entire computation."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": true,
+     "input": [
+      "%%timeit -n1 -r1\n",
+      "\n",
+      "async_results = []\n",
+      "for strike in strike_vals:\n",
+      "    for sigma in sigma_vals:\n",
+      "        # This line submits the tasks for parallel computation.\n",
+      "        ar = view.apply_async(price_option, price, strike, sigma, rate, days, paths)\n",
+      "        async_results.append(ar)\n",
+      "\n",
+      "c.wait(async_results)  # Wait until all tasks are done."
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "1 loops, best of 1: 3.75 s per loop\n"
+       ]
+      }
+     ],
+     "prompt_number": 16
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "len(async_results)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "pyout",
+       "prompt_number": 18,
+       "text": [
+        "30"
+       ]
+      }
+     ],
+     "prompt_number": 18
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "## Process and visualize results"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Retrieve the results using the `get` method:"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": true,
+     "input": [
+      "results = [ar.get() for ar in async_results]"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 19
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Assemble the result into a structured NumPy array."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": true,
+     "input": [
+      "prices = np.empty(n_strikes*n_sigmas,\n",
+      "    dtype=[('ecall',float),('eput',float),('acall',float),('aput',float)]\n",
+      ")\n",
+      "\n",
+      "for i, price in enumerate(results):\n",
+      "    prices[i] = tuple(price)\n",
+      "\n",
+      "prices.shape = (n_strikes, n_sigmas)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 20
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Plot the value of the European call in (volatility, strike) space."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.figure()\n",
+      "plt.contourf(sigma_vals, strike_vals, prices['ecall'])\n",
+      "plt.axis('tight')\n",
+      "plt.colorbar()\n",
+      "plt.title('European Call')\n",
+      "plt.xlabel(\"Volatility\")\n",
+      "plt.ylabel(\"Strike Price\")"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "pyout",
+       "prompt_number": 21,
+       "text": [
+        "<matplotlib.text.Text at 0x10ab98690>"
+       ]
+      },
+      {
+       "output_type": "display_data",
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j2oag9ADqwTDTw+yxai44rPuRS8HPQEG1Zdv89a9/RWRkJF5//XU89thjBgtUU2SJc0RE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\n"
+      }
+     ],
+     "prompt_number": 21
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Plot the value of the Asian call in (volatility, strike) space."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.figure()\n",
+      "plt.contourf(sigma_vals, strike_vals, prices['acall'])\n",
+      "plt.axis('tight')\n",
+      "plt.colorbar()\n",
+      "plt.title(\"Asian Call\")\n",
+      "plt.xlabel(\"Volatility\")\n",
+      "plt.ylabel(\"Strike Price\")"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "pyout",
+       "prompt_number": 22,
+       "text": [
+        "<matplotlib.text.Text at 0x1088bf150>"
+       ]
+      },
+      {
+       "output_type": "display_data",
+       "png": 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gmJVjmG9x3zgzzMpJeg8gFoZZGUa5JveLM6OsDknvAcTBKCvHMNfmXnFmmJWT9B5ALAyz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\nA/p/fJgkSzip6OsAAAAASUVORK5CYII=\n"
+      }
+     ],
+     "prompt_number": 22
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Plot the value of the European put in (volatility, strike) space."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.figure()\n",
+      "plt.contourf(sigma_vals, strike_vals, prices['eput'])\n",
+      "plt.axis('tight')\n",
+      "plt.colorbar()\n",
+      "plt.title(\"European Put\")\n",
+      "plt.xlabel(\"Volatility\")\n",
+      "plt.ylabel(\"Strike Price\")"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "pyout",
+       "prompt_number": 14,
+       "text": [
+        "&lt;matplotlib.text.Text at 0x106d34150&gt;"
+       ]
+      },
+      {
+       "output_type": "display_data",
+       "png": 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95UvNs2bN4s9//jOhoaGMGDGCY8eOBaJUF081l5eXM3HiRFq1asXs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\nQmCC\n"
+      }
+     ],
+     "prompt_number": 14
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Plot the value of the Asian put in (volatility, strike) space."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.figure()\n",
+      "plt.contourf(sigma_vals, strike_vals, prices['aput'])\n",
+      "plt.axis('tight')\n",
+      "plt.colorbar()\n",
+      "plt.title(\"Asian Put\")\n",
+      "plt.xlabel(\"Volatility\")\n",
+      "plt.ylabel(\"Strike Price\")"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "display_data",
+       "png": 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+      }
+     ],
+     "prompt_number": 15
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
  No newline at end of file